orthogonal series

orthogonal series

[ȯr¦thäg·ən·əl ′sir‚ēz]
(mathematics)
An infinite series each term of which is the product of a member of an orthogonal family of functions and a coefficient; the coefficients are usually chosen so that the series converges to a desired function.
References in periodicals archive ?
The orthogonal series for F(z) given in (9) may be directly used to define an estimator of f([theta]).
Efromovich, "Orthogonal series density estimation," Wiley Interdisciplinary Reviews: Computational Statistics, vol.
Ellingwood, "Orthogonal series expansions of random fields in reliability analysis," Journal of Engineering Mechanics, vol.
To some extent, especially in the Orthogonal series, this may be true, but Burnham's treatment of more speculative stories such as "Axiomatic," "Learning to be Me," and "Unstable Orbits in the Space of Lies" shows a peculiar blindness to how the conceptual developments actually connect to the unfolding of plot.
The course was on Orthogonal Series, in fact it was more linked to his monograph on Hilbert Spaces [6], published in 1956, with a Note by I.
Grigorian, On the representation of functions by orthogonal series in weighted [L.sup.p] spaces, Studia.
Grigorian, Universal or quasiuniversal in [L.sup.p.sub.[0,1]] orthogonal series, Journal of Contemporary Mathematical Analysis, 35:4(2000), 44-64.
Although several properties and applications of orthogonal series with respect to a vector measure are known ([13, 14, 21]), the question of the almost everywhere convergence of series defined by such functions has not been studied yet.
In practice, the effectiveness of the algorithms hinges on their stability behavior and the rate at which the underlying orthogonal series expansions converge to the exponential function.
[28] YUAN XU, Summability of Fourier orthogonal series for Jacobi weight on a ball in Rd, Trans.
GILBERT, Maximal theorems for some orthogonal series.I., Trans.

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